I'm not sure if someone has done the exact experiment you're looking for, but I remembered that in "Spectral Analysis of the Ear," Goupell & Hartmann used a technique
called “enhancement” to demonstrate that human ears can distinguish up
to the 69 harmonic and point out that Plomp and Mimpen (The ear as a
frequency analyzer II) identified the 5th and 7th harmonic as the upper
limit for ear resolution, also Berstein and Oxenham (Pitch
discrimination of diotic and dichotic tone complexes: Harmonic
resolvability or harmonic number?) Identified the 10th harmonic. Maybe that would be a good reading to start with.